In this paper, we will need to impose point constraints at marked points. Ordinarily, evaluation morphisms \(\mathcal {M}(X,\beta ) \rightarrow \underline{X}\)  on underlying stacks do not lift to morphisms of log stacks. For our purposes however, we will only need to impose point constraints at contact order 0 points, which mitigates many of these difficulties. Indeed, by [1]} Proposition \(3.3\) , we have a morphism of log stacks \(\mathcal {M}(X,\beta ) \rightarrow {P}(X,0) = X \times B\mathbb {G}_m\) , with \(B\mathbb {G}_m\)  equipped with the trivial log structure. The projection map on underlying stacks lifts to a map of log stacks, and thus equips \(\mathcal {M}(X,\beta ) \rightarrow \underline{X}\)  with the structure of a log map.
